Solve 5/sqrt{50}

$$\frac { 5 } { \sqrt { 50 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{5}{5\sqrt{2}}$$

Rationalize the denominator of \frac{5}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{2}}{5\times 2}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\sqrt{2}}{2}$$